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Computing Equilibria in Finance Economies

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  • Herings,P. Jean-Jacques
  • Kubler,Felix

    (METEOR)

Abstract

The general equilibrium model with incomplete asset markets provides a unified framework for many problems in finance and macroeconomics. In its simplest version with only two time periods and a single physical commodity the model is ideally suited for the study of problems in cross sectional asset pricing and portfolio theory. In this paper we develop a homotopy algorithm to approximate equilibria in these ''finance economies''. Since the algorithm is tailor made for finance economies, the number of nonlinear equations that has to be solved for, and therefore the computing time,is an order of magnitude smaller than that of existing general purpose algorithms.The algorithm is shown to be generically convergent. We implement the algorithm using HOMPACK. To illustrate its performance, we present various numerical examples and report running times.

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Bibliographic Info

Paper provided by Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR) in its series Research Memorandum with number 010.

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Date of creation: 2002
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Handle: RePEc:unm:umamet:2002010

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Keywords: Economics ;

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References

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  1. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
  2. Jean-Jacques Herings, P., 1997. "A globally and universally stable price adjustment process," Journal of Mathematical Economics, Elsevier, vol. 27(2), pages 163-193, March.
  3. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702, April.
  4. R. Mehra & E. Prescott, 2010. "The equity premium: a puzzle," Levine's Working Paper Archive 1401, David K. Levine.
  5. Talman, A.J.J. & Doup, T.M. & Laan , G. van der, 1987. "The (2**(n+1)-2)-ray algorithm: A new simplicial algorithm to compute economic equilibria," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153107, Tilburg University.
  6. Hens,Thorsten, 1991. "Structure of general equilibrium models with incomplete markets and a single consumption good," Discussion Paper Serie A 353, University of Bonn, Germany.
  7. Brown, Donald J & DeMarzo, Peter M & Eaves, B Curtis, 1996. "Computing Equilibria When Asset Markets Are Incomplete," Econometrica, Econometric Society, vol. 64(1), pages 1-27, January.
  8. Herings, P.J.J. & Kubler, F., 1999. "The Robustness of the CAPM - A Computational Approach," Discussion Paper 1999-54, Tilburg University, Center for Economic Research.
  9. Schmedders, Karl, 1998. "Computing equilibria in the general equilibrium model with incomplete asset markets," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1375-1401, August.
  10. Eaves, B. Curtis & Schmedders, Karl, 1999. "General equilibrium models and homotopy methods," Journal of Economic Dynamics and Control, Elsevier, vol. 23(9-10), pages 1249-1279, September.
  11. Demarzo, Peter M. & Eaves, B. Curtis, 1996. "Computing equilibria of GEI by relocalization on a Grassmann manifold," Journal of Mathematical Economics, Elsevier, vol. 26(4), pages 479-497.
  12. Herbert E. Scarf, 1967. "The Approximation of Fixed Points of a Continuous Mapping," Cowles Foundation Discussion Papers 216R, Cowles Foundation for Research in Economics, Yale University.
  13. Herings,O. Jean-Jacques & Kubler,Felix, 2000. "The Robustness of CAPM-A Computational Approach," Research Memorandum 035, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
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Cited by:
  1. Talman, A.J.J. & Thijssen, J.J.J., 2006. "Existence of equilibrium and price adjustments in a finance economy with incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 42(3), pages 255-268, June.
  2. Mercedes Esteban-Bravo, 2004. "An Interior Point Algorithm For Computing Equilibria In Economies With Incomplete Asset Markets," Business Economics Working Papers wb046023, Universidad Carlos III, Departamento de Economía de la Empresa.
  3. Jacco Thijssen, 2008. "A computational study on general equilibrium pricing of derivative securities," Annals of Finance, Springer, vol. 4(4), pages 505-523, October.
  4. Kubler, Felix & Schmedders, Karl, 2010. "Competitive equilibria in semi-algebraic economies," Journal of Economic Theory, Elsevier, vol. 145(1), pages 301-330, January.
  5. Herings,P. Jean-Jacques & Kubler,Felix, 2003. "Approximate CAPM When Preferences Are CRRA," Research Memorandum 064, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  6. Herings, P.J.J. & Kubler, F., 1999. "The Robustness of the CAPM - A Computational Approach," Discussion Paper 1999-54, Tilburg University, Center for Economic Research.

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